The present invention is directed to a battery of multifractal-based tests developed for the analysis of electrocardiogram (EKG) data. The invention is preferably for clinical use in a novel integrated approach to diagnosis of heart disease, prognosis of cardiac conditions, and monitoring of heart disease therapies. This multifractal approach is not available with current, clinically available cardiographic methods.
Cardiovascular disease currently affects approximately 20 million Americans. Roughly 12 million Americans are affected by coronary artery disease (CAD), and 5 million suffer from congestive heart failure (CHF). More importantly, millions suffer from undiagnosed heart disease; the prevalence of undiagnosed CHF is estimated to be approximately 20 million in the U.S. In addition, 400,000 Americans with CAD or CHF die from sudden cardiac death each year. Although there are a number of conventional nonfractal tests for the diagnosis of heart disease (several of them highly invasive), none of these tests can effectively predict which patients in this group of 17 million (CAD+CHF) are at risk of sudden death. Since it is impractical and undesirable to treat every person with heart disease (CAD or CHF) as if such a person were at risk for sudden death, a reliable predictive test (or test battery) to determine which patients are at high risk would be of great value.
In addition, new drugs and other treatments continue to be developed to treat heart disease. There are, however, no currently available analytic test regimens to rapidly evaluate how well the patient may respond to treatment and whether the risk of sudden death has been decreased by anti-arrhythmic therapy. As a result, the efficacy of these treatments must be determined empirically with slow, multi-year, prospective-controlled studies, which are very difficult to extrapolate to each individual patient. Therefore, an analytic method that would monitor a patient for signs of potential improvement on therapy would also be of great value. The diagnosis of CAD and CHF would also be greatly improved by a very sensitive and specific but noninvasive test to replace or supplement expensive and invasive modalities like heart catheterization and allow screening of patients with asymptomatic heart disease.
Over the last decade, considerable promise has been demonstrated in this field by the application of one-dimensional fractal time series analysis methods to RR-interval EKG data. Fractal scaling techniques have been employed to demonstrate that the human heart beat has fractal scaling characteristics, and that this was altered by disease. These analyses used relatively simple techniques to analyze the fractality, which may be termed “monofractal” analysis. Most clinical EKG studies utilized pre-wavelet technology, Detrended Fluctuation Analysis (DFA) for analysis of short term (<11 beat) or intermediate to long term (>11 beat) monofractal scaling analysis. We will subsequently describe >11 beat (long term) analyses in the literature as LTAlpha, and <11 beats (short term) analyses as STAlpha. These early studies have revealed clinical interpretations never before seen in conventional methods of EKG analysis, permitting some limited degree of differentiation between patients with heart disease and those without.
DFA analysis has also shown that patients with congestive heart failure (CHF) have an elevated DFA LTalpha scaling coefficient when compared with normals. These abnormalities tended to normalize at night within a few hours, as would be expected from a physiologic standpoint. Other researchers have noted a similar LTalpha diurnal rhythm in normal subjects.
More recently, several authors have noted the prognostic and diagnostic value of the STalpha scaling coefficient. A prospective study of 69 heart failure patients showed that the short term DFA STalpha revealed diagnostic information not extractable from traditional methods of heart variability analysis. This study is described in K.K.L. Ho et al., “Predicting Survival in Heart Failure Case and Control Subject by Use of Fully Automated Methods for Deriving Nonlinear and Conventional Indices of Heart Rate Dynamics,” Circulation 1997;96:842-848, which is incorporated herein by reference. A separate study examined STalpha analysis of three groups of 45 patients each: (1) normals, (2) post myocardial infarction (post-MI) with ventricular tachycardia (v-tach) or electrically inducible v-tach, and (3) post-MI without v-tach or electrically inducible v-tach, revealing that the STalpha was significantly reduced in the post-MI v-tach group. This suggested that the STalpha reduction may be related to vulnerability to v-tach. This study is described in T. H. Makikallio et al., “Dynamic Analysis of Heart Rate May Predict Subsequent Ventricular Tachycardia after Myocardial Infarction,” American Journal of Cardiology Sep. 15, 1997;80(6):779-83. The STalpha was also studied in 38 patients with stable angina, but no prior MI or meds against 38 control subjects, and was shown to be a better predictor than other heart rate variability parameters. This work is described in T. H. Makikallio et al., “Heart Rate Dynamics in Patients with Stable Angina Pectoris and Utility of Fractal and Complexity Measures,” American Journal of Cardiology Jan. 1, 1998;81(1):27-31. A follow-up study of 414 post-MI patients with depressed contractility or ejection fraction (EF) of 35% showed that a reduced STalpha was the most powerful predictor of mortality of all available statistical EKG analytic methods. This work is described in H. V. Huikuri et al., “Fractal Correlation Properties of R—R Interval Dynamics and Mortality in Patients with Depressed Left Ventricular Function after an Acute Myocardial Infarction,” Circulation 2000;101:47-53. A 4-year, prospective study of 159 patients with 35% EF post-MI showed that a reduced STalpha was the best predictor of mortality; this work is described in T. H. Makikallio et al., “Fractal Analysis of Heart Rate Dynamics as a Predictor of Mortality in Patients with Depressed Left Ventricular Function after Acute Myocardial infarction. Trace Investigators. TRAndolapril Cardiac Evaluation,” American Journal of Cardiology Mar. 15, 1999;83(6):836-9. Another Danish study followed 499 patients with CHF and EF of <35%. During a followup period of 665 days, and after adjusting for age, functional class, medication, and EF, a reduced short-term alpha remained an independent predictor of mortality, RR 1.4 (95% Cl 1.0-1.9, P<0.05). This result is described in T. H. Makikallio et al., “Fractal Analysis of Time- and Frequency-Domain Measures of Heart Rate Variability as Predictors of Mortality in Patients with Heart Failure,” American Journal of Cardiology Jan. 15, 2001;87(2):178-82. Lastly, a wavelet based (non-DFA) STalpha analysis revealed that in 428 post-MI patients with 105 controls studied over a 2000-day period, the STalpha had the best Kaplan-Meyer survival statistics, when compared to other EKG based statistical tests. This work is described in Y. Ashkenazy et al., “Scale Specific and Scale Independent Measures of Heart Rate Variability as Risk Indicators,” Los Alamos arXiv:physics/9909029 Sep. 17, 1999. Hence, it is reasonable to conclude that a decreased STalpha fractal scaling coefficient has diagnostic value in predicting risk of sudden death.
Other work has demonstrated the clinical value of the DFA STalpha in monitoring response to drug therapy, and prediction of runs of abnormal beats from atrial fibrillation. A STalpha study of the effect of Atenolol therapy in advanced CHF patients revealed changes after three months, but other statistical EKG parameters and intermediate to LTalpha did not change This study is described in L. Y. Lin et al., “Reversal of Deteriorated Fractal Behavior of Heart Rate Variability by Beta-Blocker Therapy in Patients with Advanced Congestive Heart Failure,” Journal of Cardiovascular Electrophysiology Jan. 12, 2001 (1):26-35. A study of patients at risk for spontaneous atrial fibrillation revealed that both approximate entropy (ApEn) and STalpha decreased approximately 20 minutes before atrial fibrillation, but traditional heart variability methods did not, as described in S. Vikman et al., “Altered Complexity and Correlation Properties of R—R Interval Dynamics before the Spontaneous Onset of Paroxysmal Atrial Fibrillation,” Circulation 1999;100:2079-2084. This raises the possibility that STalpha measures a fundamental property of cardiac function, as low values of STalpha correlate with poor survival in Ml patients with low EF, and may predict risk of atrial fibrillation.
A newer, more powerful method of fractal analysis termed wavelet-based multifractal analysis has recently been applied to EKG data. We call this type of analysis multifractal (MF) Holder analysis herein, although earlier works may often use the Hurst coefficient interchangeably with the related Holder coefficient. The MF Holder analysis of human EKGs was described by a Boston University team in P. C. Ivanov et al., “Multifractality in Human Heartbeat Dynamics,” Nature Vol. 399, pp. 461-465 (1999), which is incorporated herein by reference. This team examined the multifractal scaling properties of EKG RR intervals for intervals >16 beats, roughly equivalent to the DFA LTalpha analysis described above. Unlike the earlier DFA (high-pass filter type) monofractal analysis, the analysis is performed in more sophisticated, narrowly defined wavelet bands. A spectrum of local fractal scaling coefficients is generated for each time series snapshot analyzed, enhancing the potential richness of the data analysis. This continuum of scaling coefficients generates new parameters not available with monofractal EKG time-series analysis. No information is lost by this analysis, because if the signal is truly monofractal, the analysis reduces to the monofractal situation.
The Boston University analysis also revealed that the fractal pattern of the human heartbeat was much more complex than previously described. The authors concluded that the EKG data in congestive heart failure (CHF) patients was monofractal, and the normal control subjects were multifractal. These observations are crucial to the fractal analysis of EKG time series, indicating that the previously described monofractal analysis may be inadequate in characterizing the richness of the fractal behavior of the human EKG, and in detecting heart disease with a high sensitivity. Furthermore, this multifractal analysis may also offer new diagnostic features not appreciated in the monofractal methods. It is our belief that the degree of multifractality of the healthy heartbeat reflects the healthy cardiac system's greater adaptability to change, and that the loss of multifractality in heart disease is associated with failure to adapt to the external environment.
The same Boston University group also analyzed the effect of nerve control mechanisms of the heart on the multifractal nature of the human heartbeat in L. A. N. Amaral, et al., “Behavioral-Independent Features of Complex Heartbeat Dynamics,” Los Alamos arXiv:cond-mat/0106508 v1 Jun. 25, 2001 (originally published at Physical Review Letters Vol. 86, No. 26, pp. 6026-6029 (2001)), which is incorporated herein by reference. The group was able to show that blockade of sympathetic and parasympathetic nerve input into the heart by drugs significantly decreased the level of multifractal complexity.
A critical limitation of the multifractal analysis described above is that the Boston University group only pre-filtered aberrant beats up to a maximum of 2% of the total time series, and the <16 beat scaling region was excluded. We have discovered, however, that (1) 11 out of 47 of the heart disease patients we studied have 5% or more abnormal beats; (2) these beats can adversely affect the MF Holder coefficient; and (3) these beats falsely elevate our multifractal cascade coefficient MFCC (described below). These abnormalities are not seen in our 12 normal control patients, and are not removed by the pre-filtering method described in this prior art. Examination of representative “raw” RR-interval data can be very impressive in patients with such abnormal beats, as a well-defined heart rate may not be evident unless 8- or more beat smoothing is performed first.
The presence of the abnormal or arrhythmic beats appears to generate a phenomenon called intermittency, namely that the fractal behavior of the time series is disrupted by the presence of abnormal beat events. The prior art prefiltering methods as described herein consist of removing 2% or less abnormal beats. In most cases this is done by removing (prefiltering) the RR-interval beats that exceed so many standard deviations from a reference value, often based on a 5-10 beat moving average, so that the outliers can be identified. The 2% prefiltering limit consensus is apparently based on the assumption that more abnormal beats could cause distortion of the MF Holder scaling coefficient, or other fractal scaling coefficients such as the ST DFA alpha, or LT DFA alpha. We have also discovered that as little as a 1% incidence of abnormal beats can adversely affect the multifractal scaling coefficient if they are tightly clustered in time. Prior art anomalous beat filtering methods will not work in this situation, as the clustered abnormal beats could represent 10% or more of the fractal signal in some regions of the RR-beat series.
In summary, the prior art methods of removing abnormal beat intermittency effects may not work in patients with 2% or more abnormal beats, or in other situations where the abnormal beats are clustered in time. As we have discovered, these abnormal beats are quite common in clinical practice. Thus a practical method for (1) detecting abnormal beats, (2) detecting the presence of beat clustering, and (3) removing the sequelae of these abnormal beats is needed.
Still another limitation of the prior art is that there is no formal attempt to quantify the multifractal nature of the human heartbeat. Healthy patients were described as being multifractal, and heart disease patients as monofractal, but this information was not quantified. We have found that in the real world of clinical practice, some degree of multifractality is always present, although it is more prominent in some patients than in others.
Lastly, the MF Holder approach has to date only been applied to the LT (long term) >16 beat scaling region. Each of these limitations of the prior art are overcome by the present invention as described below.